Ok so I've read about half of the comments here, and I feel like now is the right time to write my first post after being a long time lurker. To make my credentials clear, I have a Masters degree in physics from a good British university so I (should) know more about many of these topics than the majority, although I hope no one takes this as an argument from authority.
Firstly, on the questions. If I were asked whether the universe started with a big explosion, I would have to say no. The Big Bang really refers to the expansion of spacetime and wasn't really an explosion as most would understand it. It was poorly worded and you may well have got people answering no who understand this distinction and who thought that the question was trying to catch out this common misconception of what the Big Bang is.
Does the Earth orbit the Sun? Well, kind of. If you had a 2 body Earth-Sun system, both bodies would orbit around the centre of mass of the whole system, which happens to be quite close to the centre of the Sun. As it is, it's even more complex than that because of the rest of the matter in the solar system. However, unless you're deliberately being facetious you'd answer this questions correctly in the survey.
As to the definition of theory, this is butchered by nearly everyone. A theory isn't something that might be right but is uncertain. It also isn't, as many scientifically minded people like to suggest, something that's very strongly supported by the available evidence. This wouldn't explain purely mathematical theories, such as set theory or group theory, which have no "evidence" as such. It also doesn't explain something like Newton's theory of Gravitation, which is known to be incorrect, but is still a perfectly valid theory. Or the various mutually incompatible string theories which are all valid as theories, but have essentially zero evidentiary evidence.
A theory is essentially just a framework of axioms, or rules, that are used to make our lives easier. In science, theories tend to be used to try and explain the world as we see it. The axioms usually come after some observations but can then be used to predict future, as yet unencountered events. So Newton's theory of gravitation is based on the axiom that any two massive bodies will feel a force of attraction that is proportional to the product of the masses of the two bodies and inversely proportional to the square of their separation. This is a perfectly good theory and asking whether it's right or wrong is the wrong question.The question is, is it useful? The answer is, yes, in many circumstances, it's extremely useful, so we use it, even though we know it's limited to slow moving, medium sized bodies. Einsteins theory of gravity is based on different axioms (too complicated to properly discuss in a comments section) that more accurately describe the universe but this too has limitations.
It should be noted that Einstein's theory of gravity gets the same results as Newton's for most everyday calculations. Newton wasn't completely wrong, his theory has great predictive value. I strongly recommend Asimov's Relativity of Wrong.
Sorry for the length, and if anyone disagrees with my take on what a theory is, let me know. I haven't given this comment a huge amount of thought. I might comment on the evolution and Big Bang questions (particularly the latter) in more detail later, especially if anyone would like to know very briefly why Physicists accept the Big Bang theory (essentially) unreservedly)
TLDR: The questions are poorly worded and most people don't really understand what a theory is, although creationists must have had the trite "Evolution is only a theory" line debunked so many times by now that they must just be spouting it to annoy people. I can't emphasise enough that it has nothing to do with how likely something is to be true. At all.
